Where to start...
+1 for Vegemite and Avocado! It's AWESOME!
What to do in (and around) SE Qld.
I don't like the Gold Coast much - as noted by others it is a tourist trap - sort of a cross between Orlando, Miami & Las Vegas, but there are some things worth seeing/doing.
Go to the beach for an early morning swim - you don't need to (and shouldn't!) go in very deep, but as long as you get your head under at some stage it's the best way to start the day!
Also, go to one of the wildlife sanctuary's - either Currumbin, Lone Pine or Australia Zoo (Nth of Brisbane).
Byron Bay is a nice little drive - check out the light house for a great view!
Eating out.
I second Tukka in Brisbane's West End - it's a must do as they have both the animals on our National coat of arms (Emu and Kangaroo), as well as Crocodile on the menu. I seem to remember that you don't eat meat though??? I think you are allowed to while travelling -isn't that one of the rules?
If you do fancy a steak, you should try to get to the Breakfast Creek Hotel (lunch or dinner) for a feed! You have to order right at the kitchen and you can even select your own piece of meat (if you want to) as they are all displayed (under glass) in front of you. Very Carnivorous!
At a minimum I say hire a car and get away from the GC if you can - either North or South you will have a good time either way. If you make it to Brisbane (and have time) the City Cat (River Ferry) is a must do! Let me know if you want a local guide as I'd be glad to come for a ferry ride - I've been promising the kids we'd do it again...
I'd offer to be your guide for your entire stay but I've got a work trip myself starting Monday and I'm NOT prepared! 8^)

Greetings from Australia! I've been here for something like four days (I say "something like" because the time travel thing that happens when you cross the International Date Line is still confusing me), and I just love it. Anne and I are in Melbourne, which I've found to be an absoulutely wonder...